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प्रश्न
Two wires of equal length, one of copper and the other of manganin have the same resistance. Which wire is thicker?
उत्तर
Since the resistivity of alloy is greater than the resistivity of its constituents. We have resistivity of manganin greater than resistivity of copper metal.
So, Resistance `R = ρ1/A`
Where l is length and A is area of cross-section of material.
Also ρ is the resistivity of the material.
For copper, `R_c = ρ_c l_c/A_c`
and for magnanin `R_m = ρ_m l_m/A_m`
We have
`ρ_m>ρ_c`
`or ρ_m/ρ_c > 1`
`As l_c = l_m`
Dividing `R_c/R_m = (ρ_cA_m)/(ρ_mA_c)`
Again `R_c = R_m`
`therefore ρ_c A_m = ρ_mA_c`
`ρ_m/ρ_c=A_m/A_c >1`
Hence `A_m >A_c`
Or, Manganin wire is thicker.
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